# Tagged Questions

For questions regarding the mathematical analysis of voting systems and behavior. Examples include the median voter theorem or the Condorcet jury theorems.

27 views

### What is a good introductory book on Rational Choice Theory for a mathematician?

I'm interested in Rational Choice Theory as an approach to political science. Amongst other, related subjects, I'd like to know a thing or two about Arrow's impossibility theorem (and other aspects of ...
44 views

### Arrow's impossibility theorem implications [closed]

If we knew that in an unfair voting system (ie: it is known that IIA does not hold) then if (1) holds, how would we go about inferring that (2) holds and then is it possible to show that if (1) and (2)...
29 views

### Poisson vs Binomial for Voting

(this is my first post so I apologise if I am asking wrongly) I am trying to determine whether I should use poisson or binomial distribution to model american poll votes for the coming election. My ...
30 views

### Describe all irreducible voting systems with two outcomes

A situation where $n$ voters choose between two candidates can be modelized by a $n$-uple $(a_1,\ldots,a_n)\in\lbrace 0,1 \rbrace^n$, where $a_i$ denotes the wish of the $i$-th voter. So the voting ...
31 views

### Counterexample to each Arrow's axiom

I am trying to find ways that combine group preferences which hold for 3 out of the 4 Arrow's axioms. Here is what I have come up with so far: Unrestricted Domain Not sure what scheme would ...
62 views

### Analyse the US presidential election from the perspective of Arrow's theory

I want to consider the voting system against the 4 Arrow's axioms. So first the voting system simplifies to first-past-the post system where the highest polling candidate wins the election. How does ...
21 views

### name of a fairness criterion

I found the following fairness criterion in the exercises of Excursions in Modern Mathematics: If a majority of the voters have candidate X ranked last, then candidate X should not be a winner of the ...
80 views

If a planner obeys anonymity and strong Pareto principle (individual preferences carry over to the group), then the social utility function will be: $W(x)=\sum_{i=1, ..., n}U_i(x)$ i.e. summing ...
9 views

### Algorithm to determine popularity through sentiment, volume, time, and feedback

I am quite new to this space of ranking algorithms, and I'm faced with a problem. I have the following factors that will determine an entity's "popularity" ranking: Number of occurrences mentioned ...
33 views

### Show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms.

I want to show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms. Given at least three rewards, and at least two individuals, there is no ...
30 views

### Pairwise majority voting and Arrow's axioms

The following is a question on Arrow's theorem with a pairwise majority decision. The bits I was unsure about was (bi) (is the 4th condition satisfied?) and also is (bii) correct? Thanks for your help ...
20 views

### Sen's theorem on minimal liberalism

I want to solve the following question regarding Sen's theorem and preferences orderings. The bit I am having trouble with is 2b Question 1: Describe Sen's theorem ('paradox') There is no social ...
30 views

### Boolean functions and characters

I'm trying to solve this, but I have no idea how to start! I'm not even sure what the question is really asking. Can anybody rephrase this and perhaps give me pointers/solutions for one of the parts?
22 views

### Condorcet winner in an examen subject with typo

I took a course in decisional models this semester. It is delightful because it allows to understand why are the weaknesses of every decision making process. Yet, the teacher gave us an old exam ...
69 views

### Can Continuous Time Markov Chains be used as a reasonable voting system?

I just compared a couple of example elections, as given on Wikipedia to show how Condorcet-methods differ from non-Condorcet ones, to what happens if you just interpret the underlying preference ...
75 views

### Algorithm for assigning users to “buckets” according to users' preferences and ranking

Suppose there is a set of $n$ users which must each be assigned to one, and only one, of $k$ mutually exclusive "buckets". However, the number of users allocated to the $i$-th bucket must be no lower ...
39 views

### IRV failing monotonicity criterion

I am looking for the simplest possible example of instant runoff voting failing the monotonicity criterion. By “simplest possible” I mean the scenario with the fewest number of candidates $(3)$ and ...
28 views

### Gaining intuition as to why maximal lotteries use randomness to break general ties

The maximal lottery is a voting system based on choosing an optimal candidate game-theoretically. If a winner isn't clear (there is no condorcet winner), then it will return probabilities as to which ...
53 views

### What is the strategy-proofness of maximal lottery?

The maximal lottery system is a voting system based in game theory. It is based in game theory. The general idea is that it is better than all the other voting systems. My question is, is it ...
33 views

### Voting Systems without tactical voting

Which voting systems do not have tactical voting? Specifically, expressing your true preference on a ballot will not result in a less favorably outcome. I'm looking at both multiple-winner and single-...
15 views

### For which voting system are multiple parties stable?

Most voting systems gravitate to two parties over time (namely, there is a bias to two candidates receiving a disportionate amount of votes.) For which voting systems does this not occur, i.e. ...
18 views

### Formula/theory to detect the desired number of workshop topics

I need to prepare a workshop and at the end of the workshop I want participants to choose from a set of questions (e.g. n=20) only x (e.g. x=5) questions to discuss. Therefore I want to give each ...
22 views

54 views

### Condorcet winner and pluralism by 51%

Is it possible for the winner by pluralism to not be the Condorcer winner, if the winner by pluralism wins by 51%? This assumes 3 or more candidates. Also this assumes a rank and or preferential ...
47 views

### Are the following two definitions of Borda winner equivalent?

The Borda count is a method used to determine the winner object where people rank objects. For instance, imagine each person ranking 3 objects. The highest ranked object gets 2 points, the second gets ...
44 views

### Normalizing votes based on source's rank

If article a from source A has 100 votes, and article b from source B has 10 votes, without simply saying that article a is better because it was voted more, how can I normalize the weight of these ...
792 views

### Game Theory Voting

I am having some difficulty in solving the following problem. I was wondering whether someone would be kind enough to sketch a solution or even better to solve the whole game. Thanks Suppose that ...
70 views

### Fair continuous election algorithm in a limited set of users

I have an election method in mind, don't know if already exists but I think there must be. It is used in a finite set of users and continuous. Every round, somebody is picked randomly depending on ...
84 views

### Calculate the Ranks of Candidates based on Votes and Total Candidates

What is the formula to calculate the rank of each candidate when I have the total candidates and votes secured by each? I've managed the percentage part, but calculating the rank has me stuck. Id be ...
83 views

### Counting in Arrow's theorem

I seem to be really confused with the counting system in Arrow's theorem. Can I have a simple explanation how they determine the outcome? I can't determine the outcome using rules from my notes. It ...
112 views

### Why not n=2 in Arrow's theorem

Why in the statement of Arrow's impossibility theorem we omit the case n=2? I will appreciate it if you can explain it in easy words. I'm by no means an expert in the area (I think it's very much ...
90 views

### Photo Rating System based of Community 'Likes'

I'm hoping to get some assistance from some math gurus on a troubling problem i'm having with a website. The site has a very large gallery (millions of photos) which are uploaded by users. The users ...
83 views

### Decide the most favorable candidate

Consider an election voting process where people need to elect a representative among n number of candidates. Is there an approach to determine the most favorable option? Voting just a single person ...